nextprime

Next prime number

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Syntax

nextprime(m)

Description

nextprime(m) returns the smallest prime number larger than or equal to m.

If the argument m is an integer, then nextprime returns the smallest prime number larger than or equal to m. A symbolic call of type "nextprime" is returned, if the argument is not of type Type::Numeric. An error occurs if the argument is a number that is not an integer.

The first prime number is 2.

Examples

Example 1

The first prime number is computed:

nextprime(-13)

If the argument of nextprime is a prime number, this number is returned:

nextprime(11)

We compute a large prime:

nextprime(56475767478567)

Symbolic arguments lead to a symbolic call:

nextprime(x)

Parameters

m

An arithmetical expression

Return Values

Prime number or a symbolic call to nextprime.

References

Michael O. Rabin, Probabilistic algorithms, in J. F. Traub, ed., Algorithms and Complexity, Academic Press, New York, 1976, pp. 21-39.

Algorithms

nextprime uses a fast probabilistic prime number test (Miller-Rabin test) to decide if the computed result is a prime number. The result returned by nextprime is either a prime number or a strong pseudo-prime for 10 randomly chosen bases.

See Also

MuPAD Functions